冻结岩体裂隙冻胀扩展的相场法模拟

Phase-field modeling of frost propagation of cracks for rock mass under frost action

寒区岩体冻结时,裂隙水相变成冰体积膨胀,冰-岩相互作用常引起裂隙冻胀扩展。为探索冻结岩体裂隙冻胀扩展的模拟和预测方法并深入认识不同条件下裂隙冻胀扩展规律,引入以弥散化标量场表征裂隙的相场法描述裂隙冻胀扩展,利用等效热膨胀系数法施加裂隙冰相变膨胀,在COMSOL Multiphysics软件平台实现对岩体裂隙冰-岩相互作用力学场控制方程和裂隙冻胀扩展相场演化控制方程的求解。基于冻结岩体冻胀扩展试验,对多种工况下裂隙冻胀扩展进行相场法模拟。模拟所得不同倾角、外荷载作用下单裂隙冻胀扩展,及不同岩桥倾角、裂隙夹角工况时双裂隙冻胀扩展均与试验获得裂隙冻胀扩展形态接近,说明文中建立的相场法模型能够较准确地模拟预测冻结岩体的裂隙冻胀扩展。受外荷载作用时,单裂隙冻胀扩展向荷载作用方向偏转。对不同岩桥倾角的双裂隙,因裂隙之间相互作用,裂隙内尖端冻胀扩展总是向另一条裂隙方向偏转,裂隙外尖端则产生共面冻胀扩展。对不同夹角的双裂隙,平行双裂隙会形成两条独立呈“蝶状”的冻胀扩展裂隙,而具有倾斜交角的双裂隙会形成交于一点的辐射状冻胀扩展裂隙。

As the rock masses in cold regions freeze,water in cracks turns into ice and expands in volume,and the mechanical interaction between ice and rock may lead to the frost propagation of cracks.To study the prediction method for the frost propagation of cracks and further cognize the laws of the frost propagation under different conditions,the phase-field model which represents cracks in a diffusive way with a scalar field is introduced to simulate the frost propagation,and the method for the equivalent thermal expansion coefficient is utilized to simulate the volume expansion of ice in cracks due to phase transition.Moreover,the governing equations for stress field for ice-rock interaction and the governing equations of phase-field evolution for the frost propagation of cracks are solved through the COMSOL Multiphysics software.Numerical simulations with the phase-field model on the frost propagation are conducted based on a series of frost propagation experiments on the rock masses.The numerical results are similar to the experimental ones for both the frost propagation of a single crack under different dip angles and external loads,and the frost propagation of double cracks under different dip angles of rock bridge and different intersection angles.It is indicated that the phase-field model established can accurately simulate the frost propagation of cracks in the rock masses.Furthermore,when subjected to an external load,the frost propagation of a single crack deflects towards the direction of the load.For the double cracks with different dip angles of rock bridge,the frost propagation of inner tips always deflects towards the adjacent crack due to the interaction of two cracks,while the outer tips propagate approximately along the coplanar direction.For double cracks with different intersection angles,two independent new frost cracks in a butterfly shape will form when the two cracks are parallel to each other,while new frost cracks in a radiation shape will form for the double cracks with an inclined intersection angle.